Local/Short-range conformal field theories from long-range perturbation theory

TL;DR

This paper demonstrates how to derive conformal data of short-range CFTs from long-range perturbation theory using the conformal Wald identity, with applications to vector and fermionic models.

Contribution

It introduces a method to extract short-range conformal data from long-range perturbation series by applying the conformal Wald identity, validated on various models.

Findings

Re-summed perturbative series yield accurate critical exponents.

Method successfully applied to O(N) vector model.

Extended to fermionic models in different dimensions.

Abstract

We show that by imposing the conformal Wald identity, one can extract conformal data of the corresponding short-range/local CFT from the long-range perturbation theory. We first apply this to the O(N) vector model. We demonstrate that by properly re-sum the perturbative series, one gets reasonable estimations of the critical exponents of the local/short-range CFTs. We then apply this method to study fermionic models with four-fermion interactions. In 2+1 dimensions, the model has the Gross-Neveu coupling and the Thirring coupling. We also consider a 4+1 dimensional theory with a generalized Thirring coupling.